Tight upper bounds on the number of invariant components on translation surfaces

被引：0
|
作者：
Yoav Naveh
机构：
[1] Ben Gurion University,Department of Mathematics
来源：
Israel Journal of Mathematics | 2008年 / 165卷
关键词：
Singular Point; Boundary Curve; Boundary Component; Closed Geodesic; Periodic Component;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
An abelian differential on a surface defines a flat metric and a vector field on the complement of a finite set of points. The vertical flow that can be defined on the surface has two kinds of invariant closed sets (i.e. invariant components) — periodic components and minimal components. We give upper bounds on the number of minimal components, on the number of periodic components and on the total number of invariant components in every stratum of abelian differentials. We also show that these bounds are tight in every stratum.
引用
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页码：211 / 231
页数：20
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